Video Transcript
The change of displacement of two
objects with time is shown in the graph. The lines plotted on the graph are
parallel. Which of the following statements
about the speeds and velocities of the two objects is correct? (A) Both their speeds and
velocities are the same. (B) Their speeds are the same, but
their velocities are different. (C) Their velocities are the same,
but their speeds are different. (D) Both their speeds and
velocities are different.
This question is about a
displacement–time graph, and we are asked about the speeds and velocities of the two
objects whose motion is shown on the graph. We can see that the two objects,
red and blue, start at different positions. The blue object starts at a
displacement of zero and the red at some negative displacement value.
Let’s recall that the velocity of
an object is given by the slope of its line on a displacement–time graph. Two lines with equal slopes
therefore correspond to two objects moving with equal velocities. We are told that the two lines on
this displacement–time graph are parallel. That means that they have equal
slopes. Therefore, both objects have equal
velocities.
Now let’s recall that the speed of
an object is equal to the magnitude of that object’s velocity. If two objects have equal
velocities, then that means that the direction and magnitude of the velocities must
both be equal. These two objects must therefore
have velocities with equal magnitudes. That means that these two objects
have equal speeds.
So we have found that the objects
have both the same speed and the same velocity as each other. The correct answer is therefore
given in option (A). Both their speeds and velocities
are the same.
